E.3
E.4
Angle between the Sun and a PV module
As seen in Eq. (18.2), the irradiance on a PV module is given by
where is the direct normal irradiance irradiance and γ = (A M , a M )(A S , a S ) is the angle
between the surface normal and the incident direction of the sunlight. The different
variables are depicted in Figure. 18.6.
For calculating cos γ, we utilise that the scalar product of two unit vectors is equal to
the cosine of the enclosed angle. Thus, we can write,
The normal vectors are given by
where we used the relationship between Cartesian and spherical horizontal coordinates
given in Eq. (18.1). Hence, we find
Modules mounted on a tilted roof
When a module is mounted on a horizontal plane, it is easy to determine its normal n M .
However, when a module is to be mounted on an arbitrarily tilted roof things become
more complicated. We thus will calculate the normal of the module in horizontal
coordinates when the coordinates with respect to the roof are given. In fact, we have to
transform the module normal from the roof coordinate system to the horizontal coordinate
system.